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Qassim University College of Engineering Electrical Engineering Department Electronics and Communications Course: EE320 Communications Principles Prerequisite: EE301 Text Book: Simon Haykin & Michael Moher, “Communication Systems”, John Wiley, 5th edition 2010. Ref Book: Simon Haykin, “Communication Systems”, John Wiley, 4th edition, 2001. www.wiley.com/go/global/haykin Associate Prof. Dr. Ahmed Abdelwahab Communication System Information Signals The signals emitted by information sources and the signals sent over a transmission channel can be classified into two distinct categories according to their physical characteristics. These two categories encompass analog and digital signals. An analog signal conveys information through a continuous and smooth variation in time of a physical quantity such as optical, electrical, or acoustical intensities and frequencies. Well-known analog signals include audio (sound) and video messages. For example, an electric signal can vary in frequency (such as the kHz, MHz, GHz designations in radio communications), and its intensity can range from low to high voltages. As the signal travels through the channel, various imperfect properties of the channel induce impairments to the signal. These include electrical noise effects, signal distortions, and signal attenuation. The function of the receiver is to extract the weakened and distorted signal from the channel, amplify it, and restore it as closely as possible to its original signal before transmission and passing it on to the message destination. The most fundamental analog signal is the periodic sine wave, shown in Fig. 1.2. Its three main characteristics are its amplitude, period or frequency, and phase. The amplitude is the size or magnitude of the waveform. This is generally designated by the symbol A and is measured in volts, amperes, or watts, depending on the signal type. The frequency (designated by f ) is the number of cycles per second that the wave undergoes (i.e., the number of times it oscillates per second), which is expressed in units of hertz (Hz). The period (generally represented by the symbol T) is the inverse of the frequency, that is, period T = 1/f. The term phase (designated by the symbol Φ) describes the position of the waveform relative to time 0, as illustrated in Fig. 1.3. This is measured in degrees or radians (rad):180° = π rad. A basic sine wave Two further common characteristics in communications are the frequency spectrum (or simply spectrum) and the bandwidth of a signal. The spectrum of a signal is the range of frequencies that it contains. That is, the spectrum of a signal is the combination of all the individual sine waves of different frequencies which make up that signal. The bandwidth (designated by B) refers to the width of this spectrum. Example If the spectrum of a signal ranges from its lowest frequency flow = 2 kHz to its highest frequency fhigh =22 kHz, then the bandwidth B = fhigh - flow = 20 kHz. • Sources of information: Text, speech, audio, pictures, video and computer data. They are one, two or three dimensions. Information production and Human perceptual system for audio and video. • Communications networks: telephone networks and Computer networks. • Communications channels: guided propagation such as: telephone channels (two-wire, coaxial cable or optical fiber) and free propagation (wireless channels) such as: broadcasting channels, mobile channels and satellite channels Historical Dates(1) In 1837, the telegraph was perfected by Samuel Morse. In 1875, the telephone was invented by Alexander Graham Bell. In 1897, A. B. Strowger, devised the automatic step-by-step switch that bears his name; of all the electromechanical switches devised over the years, the Strowger switch was the most popular and widely used. In 1864, James Maxwell formulated the electromagnetic theory of light and predicted the existence of radio waves. In 1901, Marconi received a radio signal at Signal Hill in Newfoundland; the radio signal had originated in Cornwall, England, 1700 miles away across the Atlantic. In 1904, John Ambrose Fleming invented the vacuum-tube diode, which paved the way for the invention of the vacuum-tube triode by Lee de Forest in 1906. In 1918, Edwin H. Armstrong invented the superheterodyne radio receiver; to this day, almost all radio receivers are of this type. In 1928, the first all-electronic television system was demonstrated by Philo T. Farnsworth in 1948, the transistor was invented by Walter H. Brattain, John Bardeen, and William Shockley at Bell Laboratories. The first silicon integrated circuit (IC) was produced by Robert Noyce in 1958. During the period 1943 to 1946, the first electronic digital computer, called the ENIAC, was built at the Moore School of Electrical Engineering of the University of Pennsylvania Historical Dates (2) In 1955, John R. Pierce proposed the use of satellites for communications. In 1966, K. C. Kao and G. A. Hockham of Standard Telephone Laboratories, U.K., proposed the use of a clad glass fiber as a dielectric waveguide while the laser had been invented and developed in 1959 and 1960. The Advanced Research Project Agency Network (ARPANET), first put into service in 1971. The development of ARPANET was sponsored by the U.S. Department of Defense. The pioneering work in packet switching was done on ARPANET. In 1985, ARPANET was renamed the Internet. The turning point in the evolution of the Internet occurred in 1990 when Tim Berners-Lee proposed a hypermedia software interface to the Internet, which he named the World Wide Web. The spectacular advances in microelectronics, digital computers, and lightwave systems that we have witnessed to date, and that will continue into the future, are all responsible for dramatic changes in the telecommunications environment. The Modulation Process The purpose of a communication system is to deliver a message (information or baseband) signal from an information source in recognizable form to a user destination, with the source and the user being physically separated from each other. To do this, the transmitter modifies the message signal into a form called passband signal suitable for transmission over the channel. This modification is achieved by means of a process known as modulation, which involves varying some parameter of a carrier wave in accordance with the message signal. The receiver reconstructs as closely as possible the original message signal. This reconstruction is accomplished at the receiver by using a process known as demodulation, which is the reverse of the modulation process done at the transmitter. Types of Modulation We may classify the modulation process into continuous-wave modulation and pulse modulation. In continuous-wave (CW) modulation, a sinusoidal wave is used as the carrier. When the amplitude of the carrier is varied in accordance with the message signal, we have amplitude modulation (AM), and when the angle of the carrier is varied, we have angle modulation. The latter form of CW modulation may be further subdivided into: frequency modulation (FM) and phase modulation (PM), in which the instantaneous frequency and phase of the carrier, respectively, are varied in accordance with the message signal. In pulse modulation, on the other hand, the carrier consists of a periodic sequence of rectangular pulses. However, owing to the unavoidable presence of noise and distortion in the received signal, we find that the receiver cannot reconstruct the original message signal exactly. The resulting degradation in overall system performance is influenced by the type of modulation scheme used. Specifically, we find that some modulation schemes are less sensitive to the effects of noise and distortion than others. Continuous-Wave (CW) Modulation Why do we need modulation? • For use of practical antenna size where the length of the antenna is proportional to the signal wavelength(λ) about 1/10 of λ. Therefore, the baseband information signal spectrum needed to be translated up to a higher frequency band by means of modulations for a smaller antenna size. • For use of Multiplexing that is the process of combining several independent message signals for their simultaneous transmisson over the same channel. Multiplexing could be FDM, TDM or CDM or (WDM for optical fibers). • For use of Better signal-to-noise ratio, it is found that some modulation schemes are less sensitive to the effects of noise and distortion than others. Amplitude Modulation Consider a sinusoidal carrier wave c(t) defined by where Ac is the carrier amplitude and fc is the carrier frequency Let m(t) denote the baseband information signal that carries the specification of the message. The source of carrier wave c(t) is physically independent of the source responsible for generating m(t). Amplitude modulation (AM) is defined as a process in which the amplitude of the carrier wave c(t) is varied about a mean value, linearly with the baseband signal m(t). An amplitude-modulated (AM) wave may thus be described, in its most general form, as a function of time as follows: (2.2) where ka is a constant called the amplitude sensitivity of the AM modulator Note that the envelope of s(t) has essentially the same shape as the baseband signal m(t) provided that two requirements are satisfied: 1) The amplitude of kam(t) is always less than unity, that is, Unless the carrier wave becomes overmodulated, resulting in carrier phase reversals whenever the factor 1 + kam(t) crosses zero. The modulated wave then exhibits envelope distortion, as in Figure 2.3c. It is therefore apparent that by avoiding overmodulation, a one-to-one relationship is maintained between the envelope of the AM wave and the modulating wave for all values of time - a useful feature, as we shall see later on. The absolute maximum value of kam(t) multiplied by 100 is referred to as the percentage modulation. 2) The carrier frequency fc is much greater than the highest frequency component B of the message signal m(t), that is fc >> B Unless an envelope cannot be visualized (and therefore detected) satisfactorily. The Fourier transform of the AM wave s(t) in equation 2.2 is given by Suppose that the baseband signal m(t) is band- limited to the interval f ≤ B, as in the following Figure. The shape of the spectrum shown in this figure is intended for the purpose of illustration only. Spectrum of AM Modulated Wave Note that the BW of the baseband signal B is referred as W in the above figure. This spectrum consists of two delta functions weighted by the factor Ac/ 2 and occurring at ±fc and two versions of the baseband spectrum translated in frequency by ±fc , and scaled in amplitude by kaAc /2. 1) As a result of the modulation process, the spectrum of the message signal m(t) for negative frequencies extending from – B to 0 becomes completely visible for positive (i.e., measurable) frequencies, provided that the carrier frequency satisfies the condition fc > B; herein lies the importance of the idea of "negative" frequencies. 2) For positive frequencies, the portion of the spectrum of an AM wave lying above the carrier frequency fc is referred to as the upper sideband, whereas the symmetric portion below fc is referred to as the lower sideband. For negative frequencies, the upper sideband is represented by the portion of the spectrum below - fc and the lower sideband by the portion above –fc. The condition fc > B ensures that the sidebands do not overlap. 3) For positive frequencies, the highest frequency component of the AM wave equals fc + B, and the lowest frequency component equals fc - B. The difference between these two frequencies defines the transmission bandwidth BT , for an AM wave, which is exactly twice the message bandwidth B, that is, BT = 2B. The greatest advantage of AM: the simplicity of implementation •In the transmitter, AM is accomplished using a nonlinear device such as the switching modulator in which the combined sum of the message signal and carrier wave is applied to a diode, with the carrier amplitude being large enough to swing across the characteristic curve of the diode. Fourier analysis of the voltage developed across a resistive load reveals the generation of an AM component, which may be extracted by means of a band-pass filter. •In the receiver, amplitude demodulation is also accomplished using a nonlinear device Such as a simple and highly effective circuit known as the envelope detector. The circuit consists of a diode connected in series with the parallel combination of a capacitor and load resistor. Some version of this circuit is found in most commercial AM radio receivers. Provided that the carrier frequency is high enough and the percentage modulation is less than 100 percent, the demodulator output developed across the load resistor is nearly the same as the envelope of the incoming AM wave, hence the name "envelope detector." AM Major limitations The transmitted power and the channel bandwidth are the two primary resources of any communication system, and they should be used efficiently. •Amplitude modulation is wasteful of power: The carrier wave c(t) is completely independent of the information-bearing signal m(t). The transmission of the carrier wave therefore represents a waste of power, which means that in amplitude modulation only a fraction of the total transmitted power is actually affected by m(t). •Amplitude modulation is wasteful of bandwidth: The upper and lower sidebands of an AM wave are uniquely related to each other by virtue of their symmetry about the carrier frequency. This means that as the transmission of information is concerned, only one sideband is necessary, and the communication channel therefore needs to provide only the same bandwidth as the baseband signal. In light of this observation, amplitude modulation is wasteful of bandwidth as it requires a transmission bandwidth equal to twice the message bandwidth. To overcome these limitations, we must make certain modifications by suppressing the carrier and modifying the sidebands of the AM wave. These modifications naturally result in increased system complexity. In effect, system complexity is traded for improved use of communication resources. Three types of linear modulation are introduced to implement such modifications: The demodulated signal vo(t) is therefore proportional to m(t) when the phase error ϕ is a constant. The amplitude of this demodulated signal is maximum when ϕ = 0, and it is minimum (zero) when ϕ = ±π/2. The zero demodulated signal, which occurs for ϕ = ±π/2, represents the quadrature null effect of the coherent detector. Thus the phase error ϕ in the local oscillator causes the detector output to be attenuated by a factor equal to cos ϕ. As long as the phase error ϕ is constant, the detector provides an undistorted version of the original baseband signal m(t). In practice, however, we usually find that the phase error ϕ varies randomly with time, due to random variations in the communication channel. The result is that at the detector output, the multiplying factor cos ϕ also varies randomly with time, which is obviously undesirable. Therefore, provision must be made in the system to maintain the local oscillator in the receiver in perfect synchronism, in both frequency and phase, with the carrier wave used to generate the DSB-SC modulated signal in the transmitter. The resulting system complexity is the price that must be paid for suppressing the carrier wave to save transmitter power. A practical synchronous receiver system, suitable for demodulating DSB-SC waves, is to use the Costas receiver shown in Figure 2.9. The quadrature null effect of the coherent detector may also be put to good use in the construction of the so-called quadrature-carrier multiplexing or quadrature-amplitude modulation Quadrature Amplitude Modulation • This scheme enables two DSB-SC modulated waves (resulting from the application of two physically independent message signals) to occupy the same channel bandwidth, and then it allows for the separation of the two message signals at the receiver output. It is therefore a bandwidth-conservation scheme. • To maintain synchronization between transmitter and receiver, a pilot signal outside the passband of the modulated signal may be sent . In this method, the pilot signal typically consists of a low-power sinusoidal tone whose frequency and phase are related to the carrier wave c(t); at the receiver, the pilot signal is extracted by means of a suitably tuned circuit and then translated to the correct frequency for use in the coherent detector. Frequency Translation A modulated wave s1 (t) whose spectrum is centered on a carrier frequency f1 , and the requirement is to translate it upward in frequency such that its carrier frequency is changed from f1 to a new value f2. This requirement may be accomplished using the mixer shown in Figure 2.16. Specifically, the mixer is a device that consists of a product modulator followed by a band-pass filter. The spectrum S/( f ) of the resulting signal s/(t) at the product modulator output is shown in Figure 2.17b. The signal s/(t) may be viewed as the sum of two modulated components: one component represented by the shaded spectrum and the other component represented by the no shaded spectrum in the figure. Depending on whether the incoming carrier frequency f1 is translated upward or downward. Two different situations may be identified, as following: Up conversion, where the translated carrier frequency f2 is greater than the incoming carrier frequency f1, and the required local oscillator frequency fLO is therefore defined by f2 = fLO +f1 i.e. fLO = f2 – f1 Down conversion, where the translated carrier frequency f2 is smaller than the incoming carrier frequency f1, and the required oscillator frequency fLO is therefore defined by fLO = f1 – f2 The mixer is now referred to as a frequency-down converter. Note that in this case the translated carrier frequency f2 has to be larger than B (i.e., one half of the bandwidth of the modulated signal) to avoid sideband overlap. It is important to note that mixing is a linear operation. Accordingly, the relation of the sidebands of the incoming modulated wave to the carrier is completely preserved at the mixer output. the superheterodyne receiver consists of a radio-frequency (RF) section, a mixer and local oscillator, an intermediate- frequency (IF) section, demodulator, and power amplifier. Figure 2.32 shows the block diagram of a superheterodyne receiver for amplitude modulation using an envelope detector for demodulation. The incoming amplitude-modulated wave is picked up by the receiving antenna and amplified in the RF section which is tuned to the carrier frequency of the incoming wave. The combination of mixer and local oscillator (of adjustable frequency) provides a heterodyning function, whereby the incoming signal is converted to a predetermined fixed intermediate frequency, usually lower than the incoming carrier frequency. This frequency translation is achieved without disturbing the relation of the sidebands to the carrier; The result of the heterodyning is to produce an intermediate- frequency carrier defined by In a superheterodyne receiver the mixer will develop an intermediate frequency output when the input signal frequency is greater or less than the local oscillator frequency by an amount equal to the intermediate frequency. i.e., there are two input frequencies, namely, |fLO ± fIF| which will result in fIF at the mixer output. This introduces the possibility of simultaneous reception of two signals differing in frequency by twice the intermediate frequency. For example, a receiver tuned to 0.65 MHz and having an IF of 0.455 MHz is subject to an image interference at 1.56 MHz; indeed, any receiver with this value of IF, when tuned to any station, is subject to image interference at a frequency of 0.910 MHz higher than the desired station. Since the function of the mixer is to produce the difference between two applied frequencies, it is incapable of distinguishing between the desired signal and its image frequency. The only practical cure for image interference is to employ highly selective stages in the RF section (i.e., between the antenna and the mixer) in order to favor the desired signal and discriminate against the undesired or image signal. The effectiveness of suppressing unwanted image signals increases as the number of selective stages in the RF section increases, and as the ratio of intermediate to signal frequency increases. The IF section consists of one or more amplification stages at fixed tuned IF frequency, with a bandwidth corresponding to that required for the particular type of modulation that the receiver is intended to handle (10 KHz for AM). The IF section provides most of the amplification and selectivity in the receiver. IF section can effectively suppress adjacent channel interference because of its high selectivity which can not be achieved in RF section where it is difficult to design a tunable sharp BPF of BW = 10KHz with center frequency at radio frequency range. The output of the IF section is applied to a demodulator, the purpose of which is to recover the baseband signal. If coherent detection is used, then a coherent signal source must be provided in the receiver. The final operation in the receiver is the power amplification of the recovered message signal. In single-sideband modulation, only the upper or lower sideband is transmitted. SSB modulated wave may be generated by using the frequency discrimination method that consists of a product modulator, which generates a DSB-SC modulated wave, and a band-pass filter, which is designed to pass one of the sidebands of this modulated wave and suppress the other. For the generation of an SSB modulated signal to be possible, the message spectrum must have an energy gap centered at the origin. This requirement is naturally satisfied by voice signals, whose energy gap is about 600 Hz wide (i.e.it extends from -300 to +300 Hz). Thus, assuming that the upper sideband is retained, the spectrum of the SSB modulated signal is as shown in Figure 2.11b. In designing the band-pass filter used in the frequency-discriminator for generating a SSB-modulated wave, the use of highly selective filters, which can only be realized in practice by means of crystal resonators are required. Moreover, the following three basic requirements must be met: • The desired sideband lies inside the passband of the filter. • The unwanted sideband lies inside the stopband of the filter. • The filter's transition band, which separates the passband from the stopband, is twice the lowest frequency component of the message signal. SSB Demodulator To demodulate a SSB modulated signal s(t), we may use a coherent detector, which multiplies s(t) by a locally generated carrier and then low-pass filters the product. This method of demodulation assumes perfect synchronism between the oscillator in the coherent detector and the oscillator used to supply the carrier wave in the transmitter. This requirement is usually met in one of two ways: •A low-power pilot carrier is transmitted in addition to the selected sideband. •A highly stable oscillator, tuned to the same frequency as the carrier frequency, is used in the receiver. In the latter method, it is unavoidable that there would be some phase error ϕ in the local oscillator output with respect to the carrier wave used to generate the incoming SSB modulated wave. The effect of this phase error is to introduce a phase distortion in the demodulated signal, where each frequency component of the original message signal undergoes a constant phase shift ϕ. This phase distortion is tolerable in voice communications because the human ear is relatively insensitive to phase distortion. In particular, the presence of phase distortion gives rise to a Donald Duck voice effect. In the transmission of music and video signals, on the other hand, the presence of this form of waveform distortion is absolutely unacceptable. Multiplexing is another important signal processing operation, whereby a number of independent signals can be combined into a composite signal suitable for transmission over a common channel. Voice frequencies transmitted over telephone systems, range from 300 to 3100 Hz. To transmit a number of these signals over the same channel, the signals must be kept apart so that they do not interfere with each other, and thus they can be separated at the receiving end. This is accomplished by separating the signals either in frequency or in time. The technique of separating the signals in frequency is referred to as frequency-division multiplexing (FDM), whereas the technique of separating the signals in time is called time- division multiplexing (TDM). The input voice signal is first applied to a low-pass filter, which is designed to remove high-frequency components that do not contribute significantly to signal representation but are capable of disturbing other message signals that share the common channel. The filtered signals are then applied to modulators (usually SSB modulators) that shift the frequency ranges of the signals so as to occupy mutually exclusive frequency intervals. The necessary carrier frequencies needed to perform these frequency translations are obtained from a carrier supply. In practice, each voice input is usually assigned a bandwidth of 4 kHz. The band-pass filters following the modulators are used to restrict the band of each modulated wave to its prescribed range. The resulting bandpass filter outputs are next combined in parallel to form the input to the common channel. At the receiving terminal, a bank of band-pass filters, with their inputs connected in parallel, is used to separate the message signals on a frequency-occupancy basis. Finally, the original message signals are recovered by individual demodulators. Note that the FDM system shown in Figure 2.18 operates in only one direction. To provide for two-way transmission, as in telephony, for example, we have to completely duplicate the multiplexing facilities, with the components connected in reverse order and with the signal waves proceeding from right to left. practical implementation of FDM system The practical implementation of an FDM system usually involves many steps of modulation and demodulation, as illustrated in Figure 2.19. The first multiplexing step combines 12 voice inputs into a basic group, which is formed by having the nth input modulate a carrier at frequency fn = 60 + 4n kHz, where n = 1,2, . . . , 12. The lower sidebands are then selected by band-pass filtering and combined to form a group of 12 lower sidebands (one for each voice input). Thus the basic group occupies the frequency band 60 to 108 kHz. The next step in the FDM hierarchy involves the combination of five basic groups into a supergroup. This is accomplished by using the nth group to modulate a carrier of frequency fn = 372 + 48n kHz, where n = 1,2, . . . , 5 . Here again the lower sidebands are selected by filtering and then combined to form a supergroup occupying the band 312 to 552 kHz. Thus a supergroup is designed to accommodate 60 independent voice inputs. In a similar manner, supergroups are combined into mastergroups, and mastergroups are combined into very large groups. 2.6 -Angle Modulation Angle modulation in which the angle of the carrier wave is varied according to the baseband information signal. In this method of modulation, the amplitude of the carrier wave is maintained constant. An important feature of angle modulation is that it can provide better discrimination against noise and interference than amplitude modulation. However, this improvement in performance is achieved at the expense of increased transmission bandwidth; that is, angle modulation provides us with a practical means of exchanging channel bandwidth for improved noise performance. Such a tradeoff is not possible with amplitude modulation, regardless of its form. Basic Definitions Let θi (t) denote the instantaneous angle of a modulated sinusoidal carrier, assumed to be a function of the message signal. The resulting angle-modulated wave can be expressed as If θi (t) increases monotonically with time, the average frequency in Hertz, over an interval from t to t + Δt, is given by Where fi(t) defines the instantaneous frequency of the angle-modulated signal s(t). The angle-modulated signal s(t) may be interpreted as a rotating phasor of length Ac and angle θi (t). The angular velocity of such a phasor is dθi(t)/dt measured in radians per second. There are two commonly used methods, phase modulation and frequency modulation, in which the angle θ,(t) may be varied in some manner with the message (baseband) signal, defined as follows: Phase modulation (PM) is that form of angle modulation in which the angle θi (t) is varied linearly with the message signal m(t), as shown by The term 2πfct represents the angle of the unmodulated carrier; and the constant kp represents the phase sensitivity of the modulator, expressed in radians per volt on the assumption that m(t) is a voltage waveform. The phase-modulated signal s(t) is thus described in the time domain by Frequency modulation (FM) is that form of angle modulation in which the instantaneous frequency fi (t) is varied linearly with the message signal m(t), as shown by The term fc represents the frequency of the unmodulated carrier, and the constant kf represents the frequency sensitivity of the modulator, expressed in Hertz per volt. Therefore, the instantaneous phase can be expressed as The frequency-modulated signal is therefore described in the time domain by The envelope of a PM or FM signal is constant (equal to the carrier amplitude), whereas the envelope of an AM signal is dependent on the message signal. All the properties of PM signals can be deduced from those of FM signals and vice versa. Henceforth, we concentrate our attention on FM signals. Frequency Modulation The FM signal s(t) is a nonlinear function of the modulating signal m(t), which makes frequency modulation a nonlinear modulation process. The simplest case possible, namely, that of a single-tone modulation that produces a narrowband FM signal is first considered. Hence, Consider a sinusoidal modulating signal defined by The instantaneous frequency of the resulting FM signal equals The quantity Δf is called the frequency deviation, representing the maximum departure of the instantaneous frequency of the FM signal from the carrier frequency fc. A fundamental characteristic of an FM signal is that the frequency deviation Δf is proportional to the amplitude of the modulating signal and is independent of the modulation frequency. In a physical sense, the parameter β represents the phase deviation of the FM signal, that is, the maximum departure of the angle θi(t). from the angle 2πfct of the unmodulated carrier; hence, β is measured in radians. The FM signal itself is given By 2.33 Depending on the value of the modulation index β, we may distinguish two cases of frequency modulation: •Narrowband FM, for which β is small compared to one radian. •Wideband FM, for which β is large compared to one radian. Assuming that the modulation index β is small compared to one radian, we may use the following approximations: Equation (2.35) may be expanded as follows: This expression is somewhat similar to the corresponding one defining an AM signal, which is as follows: In the case of sinusoidal modulation, the basic difference between an AM signal and a narrowband FM signal is that the algebraic sign of the lower side frequency in the narrowband FM is reversed. Thus, a narrowband FM signal requires essentially the same transmission bandwidth (i.e.,2fm) as the AM signal. Using the complex representation of band-pass signals described in Appendix 2 of the textbook. Specifically, assume that the carrier frequency fc is large enough (compared to the bandwidth of the FM signal) to justify rewriting equation (2.33) in the form This is the desired form for the Fourier series representation of the single-tone FM signal s(t) for an arbitrary value of β. Where is called the nth order Bessel function of the first kind and argument β which are plotted in figure 2.23 for orders 0,1,2,3 & 4 versus the modulation index β. For small values of the modulation index β, we have • The spectrum of an FM signal contains a carrier component and an infinite set of side frequencies located symmetrically on either side of the carrier at frequency separations of fm , 2fm , 3fm, - . . . In this respect, the result is unlike that which prevails in an AM system, since in an AM system a sinusoidal modulating signal gives rise to only one pair of side frequencies. • For the special case of β small compared with unity, only the Bessel coefficients Jo(β) and J1(β) have significant values, so that the FM signal is effectively composed of a carrier and a single pair of side frequencies at fc ± fm , . This situation corresponds to the special case of narrowband FM that was considered earlier. • The amplitude of the carrier component varies with β according to Jo(β). That is, unlike an AM signal, the amplitude of the carrier component of an FM signal is dependent on the modulation index β. The physical explanation for this property is that the envelope of an FM signal is constant, so that the average power of such a signal developed across a 1-ohm resistor is also constant, as shown by When the carrier is modulated to generate the FM signal, the power in the side frequencies may appear only at the expense of the power originally in the carrier. The average power of an FM signal may also be determined from Equation (2.48), obtaining An approximate rule for the transmission bandwidth of an FM signal generated by a single-tone modulating signal of frequency fm as follows: This empirical relation is known as Carson's rule. A definition based on retaining the maximum number of significant side frequencies whose amplitudes are all greater than some selected Value may be used for the FM transmission bandwidth. A convenient choice for this value is 1 % of the unmodulated carrier amplitude. Consider next the more general case of an arbitrary modulating signal m(t) with its highest frequency component denoted by B. The bandwidth required to transmit an FM signal generated by this modulating signal is estimated by using a worst-case tone modulation analysis. Specifically, we first determine the so-called deviation ratio D, defined as the ratio of the frequency deviation Δf, which corresponds to the maximum possible amplitude of the modulation signal m(t), to the highest modulation frequency B; these conditions represent the extreme cases possible. The deviation ratio D plays the same role for nonsinusoidal modulation that the modulation index β plays for the case of sinusoidal modulation. Then, replacing β by D and replacing fm with B, we may use Carson's rule given by Equation (2.55) or the universal curve of Figure 2.26 to obtain a value for the transmission bandwidth of the FM signal. From a practical viewpoint, Carson's rule somewhat underestimates the bandwidth requirement of an FM system, whereas using the universal curve of Figure 2.26 yields a somewhat conservative result. Thus, the choice of a transmission bandwidth that lies between the bounds provided by these two rules of thumb is acceptable for most practical purposes. In North America, the maximum value of frequency deviation Δf is fixed at 75 kHz for commercial FM broadcasting by radio. If we take the modulation frequency B = 15 kHz, which is typically the "maximum" audio frequency of interest in FM transmission, we find that the corresponding value of the deviation ratio is Using Carson's rule, replacing β by D, and replacing fm by B, the approximate value of the transmission bandwidth of the FM signal is obtained as On the other hand, use of the curve of Figure 2.26 gives the transmission bandwidth of the FM signal to be In practice, a bandwidth of 200 kHz is allocated to each FM transmitter. There are essentially two basic methods of generating frequency-modulated signals, namely, direct FM and indirect FM. In the direct method the carrier frequency is directly varied in accordance with the input baseband signal, which is readily accomplished using a voltage-controlled oscillator (VCO). In the indirect method, the modulating signal is first used to produce a narrowband FM signal, and frequency multiplication is next used to increase the frequency deviation to the desired level. The indirect method is the preferred choice for frequency modulation when the stability of carrier frequency is of major concern as in commercial radio broadcasting. The indirect method of generating a wideband FM signal The use of crystal controlled oscillator provides frequency stability. To minimize the distortion inherent in the phase modulator, the maximum phase deviation (modulation index β) is kept small, thereby resulting in a narrowband FM signal. The implementation of the narrow-band phase modulator is described in Figure 2.21. The narrowband FM signal is next multiplied in frequency by means of a frequency multiplier so as to produce the desired wideband FM signal. Frequency Multiplier. It consists of a nonlinear device followed by a band-pass filter, as shown above. The implication of the nonlinear device being memoryless is that it has no energy-storage elements. The memoryless nonlinear device is an nth power-law device. The mid-band frequency of the band-pass filter in Figure 2.28 is set equal to nfc where fc is the carrier frequency of the incoming FM signal s(t). Moreover, the bandpass filter is designed to have a bandwidth equal to n times the transmission bandwidth of s(t). The input instantaneous frequency of the input FM wave The output instantaneous frequency of the output FM wave will be Frequency demodulation is the process that enables us to recover the original modulating signal from a frequency- modulated signal. The objective is to produce a transfer characteristic that is the inverse of that of the frequency modulator, which can be realized directly or indirectly. The direct method of frequency demodulation involves the use of a popular device known as a frequency discriminator, whose instantaneous output amplitude is directly proportional to the instantaneous frequency of the input FM signal. The indirect method of frequency demodulation uses another popular device known as a phase-locked loop. Balanced frequency discriminator The ideal frequency discriminator may be modeled as a pair of slope circuits followed by envelope detectors and finally a summer, as in Figure 4.14a. This scheme is called a balanced frequency discriminator which can be closely realized using the circuit shown in Figure 4.14b. The upper and lower resonant filter sections of this circuit are tuned to frequencies above and below the unmodulated carrier frequency fc, respectively. In Figure 4.14c the amplitude responses of these two tuned filters are plotted , together with their total response, assuming that both filters have a high Q-factor. The Q-factor is equal to the resonant frequency divided by the 3-dB bandwidth of the circuit. In the RLC parallel resonant circuits shown in Figure 4.14b, the resistance R is contributed largely by imperfections in the inductive elements of the circuits. Stereo multiplexing is a form of frequency-division multiplexing (FDM) designed to transmit two separate signals via the same carrier. It is widely used in FM radio broadcasting to send two different elements of a program (e.g., two different sections of an orchestra, a vocalist and an accompanist) so as to give a spatial dimension to its perception by a listener at the receiving end. The specification of standards for FM stereo transmission is influenced by two factors: 1. The transmission has to operate within the allocated FM broadcast channels. 2. It has to be compatible with monophonic radio receivers. The Block Diagram of the FM Stereo Multiplexing Let ml(t) and mr(t) denote the signals picked up by left-hand and right-hand microphones at the transmitter. The sum signal is left unprocessed in its baseband form; it is available for monophonic reception. The difference signal and a 38-kHz subcarrier (derived from a 19-kHz crystal oscillator by frequency doubling) are applied to a product modulator, thereby producing a DSB-SC modulated wave. In addition to the sum signal and this DSB-SC modulated wave, the multiplexed signal m(t) also includes a 19- kHz pilot to provide a reference for the coherent detection of the difference signal at the stereo receiver. Thus the multiplexed signal is described as shown below where fc = 19 kHz, and K is the amplitude of the pilot tone. FM Radio Receiver The block diagram of a superheterodyne receiver for frequency modulation is exactly as that of the AM explained in Figure 2.32 except for the FM receiver, a frequency discriminator is used for demodulation. Typical frequency parameters of commercial AM and FM radio receivers are listed in Table 2.3 above. Pulse Modulation In continuous-wave (CW) modulation, some parameter of a sinusoidal carrier wave is varied continuously in accordance with the message signal. In pulse modulation, some parameter of a pulse train is varied in accordance with the message signal. There are two families of pulse modulation: analog pulse modulation and digital pulse modulation. In analog pulse modulation, a periodic pulse train is used as the carrier wave, and some characteristic feature of each pulse (e.g., amplitude, duration, or position) is varied in a continuous manner in accordance with the corresponding sample value of the message signal. Thus in analog pulse modulation, information is transmitted basically in analog form, but the transmission takes place at discrete times. In digital pulse modulation, on the other hand, the message signal is represented in a form that is discrete in both time and amplitude, thereby permitting its transmission in digital form as a sequence of coded pulses; this form of signal transmission has no CW counterpart. The use of coded pulses for the transmission of analog information-bearing signals represents a basic ingredient in the application of digital communications. This chapter may therefore be viewed as a transition from analog to digital communications in study of the principles of communication systems. We begin the discussion by describing the sampling process, which is basic to all pulse modulation systems, whether they are analog or digital. The sampling process The sampling process is usually described in the time domain. Through use of the sampling process, an analog signal is converted into a corresponding sequence of samples that are usually spaced uniformly in time. Clearly, for such a procedure to have practical utility, it is necessary that we choose the sampling rate properly, so that the sequence of samples uniquely defines the original analog signal. This is the essence of the sampling theorem, which is derived in what follows. Where Ts is the sampling period, and its reciprocal fs = 1ITs is the sampling rate. This ideal form of sampling is called instantaneous sampling. where G ( f ) is the Fourier transform of the original signal g(t) of finite energy, which is specified for all time. Equation (3.2) states that the process of uniformly sampling a continuous-time signal of finite energy results in a periodic spectrum with a period equal to the sampling rate. The Sampling Theorem The sampling theorem for strictly band-limited signals of finite energy may be stated in two equivalent parts, which apply to the transmitter and the receiver of a pulse modulation system, respectively: • A band-limited signal of finite energy, which has no frequency components higher than B Hertz, is completely described by specifying the values of the signal at instants of time separated by (1/2B) seconds. • A band-limited signal of finite energy, which has no frequency components higher than B Hertz, may be completely recovered from a knowledge of its samples taken at the rate of 2B samples per second. • The sampling rate of 2 B samples per second, for a signal whose bandwidth of B Hertz, is called the Nyquist rate; its reciprocal 1/2 B (measured in seconds) is called the Nyquist interval. some aliasing is produced by the sampling process if the sampling frequency is less than Nyquist rate. Aliasing refers to the phenomenon of a high-frequency component in the spectrum of the signal seemingly taking on the identity of a lower frequency in the spectrum of its sampled version, as illustrated in Figure 3.3. To combat the effects of aliasing in practice, we may use two corrective measures, as described here: 1. Prior to sampling, a low-pass anti-aliasing filter is used to attenuate those high frequency components of the signal that are not essential to the information being conveyed by the signal. 2. The filtered signal is sampled at a rate slightly higher than the Nyquist rate. The reconstruction filter is a low-pass filter with • A passband extending from - W to W, which is itself determined by the anti-aliasing filter. • A transition band extending (for positive frequencies) from W to fs - W, where fs is the sampling rate. The fact that the reconstruction filter has a well-defined transition band means that it is physically realizable. In pulse-amplitude modulation (PAM), the amplitudes of regularly spaced pulses are varied in proportion to the corresponding sample values of a continuous message signal; the pulses can be of a rectangular form or some other appropriate shape. The dashed curve in fig.3.5 depicts the waveform of a message signal m(t), and the sequence of amplitude-modulated rectangular pulses shown as solid lines represents the corresponding PAM signal s(t). In digital circuit technology, two operations that are jointly called "sample and hold" involve in the generation of the PAM signal. One important reason for intentionally lengthening the duration of each sample is to avoid the use of an excessive channel bandwidth, since bandwidth is inversely proportional to pulse duration T. However, care has to be exercised in how long we make the sample duration T. In order to recover (reconstruct) the original message signal m(t), The PAM signal s(t) is passed through a LPF whose frequency response is defined in Figure 3.4c followed by an equalizer in order to compensate for the amplitude distortion. However, for a duty cycle T/Ts ≤ 0.1, the amplitude distortion is less than 0.5 percent, in which case the need for equalization may be omitted altogether. Time Division Multiplexing (TDM) An important feature of the sampling process is a conservation of time. That is, the transmission of the message samples engages the communication channel for only a fraction of the sampling interval on a periodic basis, and in this way some of the time interval between adjacent samples is cleared for use by other independent message sources on a time-shared basis resulting in a time-division multiplex (TDM) system, which enables the joint utilization of a common communication channel by a plurality of independent message sources without mutual interference among them. Synchronization is essential for a satisfactory operation of the TDM system. The way this synchronization is implemented depends naturally on the method of pulse modulation used to transmit the multiplexed sequence of samples. The TDM system is highly sensitive to dispersion in the common channel, that is, to variations of amplitude with frequency or lack of proportionality of phase with frequency. Accordingly, accurate equalization of both magnitude and phase responses of the channel is necessary to ensure a satisfactory operation of the TDM system TDM is immune to nonlinearities in the channel as a source of cross-talk. Because different message signals are not simultaneously applied to the channel. The Quantization Process The sampling process takes care of the discrete-time representation of the message signal while the quantization process takes care of the discrete amplitude representation of the message signal. A continuous signal, such as voice, has a continuous range of amplitudes and therefore its samples have a continuous amplitude range. In other words, within the finite amplitude range of the signal, we find an infinite number of amplitude levels. It is not necessary in fact to transmit the exact amplitudes of the samples. Any human sense (the ear or the eye), as ultimate receiver, can detect only finite intensity differences. This means that the original continuous signal may be approximated by a signal constructed of discrete amplitudes selected on a minimum error basis from an available set. The amplitude quantization is defined as the process of transforming the sample amplitude m(nTs) of a message signal m(t) at time t = nTs into a discrete amplitude v(nTs) taken from a finite set of possible amplitudes. the quantization process is assumed memoryless and instantaneous, which means that the transformation at time t = nTs is not affected by earlier or later samples of the message signal. This simple form of scalar quantization, though not optimum, is commonly used in practice. The signal amplitude m is specified by the index k if it lies inside the partition cell where L is the total number of amplitude levels used in the quantizer. Note that the notation is simplified by dropping the time index. The discrete amplitudes mk, k = 1, 2,. . . , L, at the quantizer input are called decision levels or decision thresholds. At the quantizer output, the index k is transformed into an amplitude vk that represents all amplitudes of the cell ; the discrete amplitudes vk, k = 1,2,. . . , L,are called representation levels or reconstruction levels, and the spacing between two adjacent representation levels is called a quantum or step-size. Thus, the quantizer output v equals vk if the input signal sample m belongs to the interval Quantizers can be of a uniform or nonuniform type. In a uniform quantizer, the representation levels are uniformly spaced; otherwise, the quantizer is nonuniform. Quantization Noise The use of quantization introduces an error defined as the difference between the input signal m and the output signal v. The error is called quantization noise. Figure 3.11 illustrates a typical variation of the quantization noise as a function of time, assuming the use of a uniform quantizer of the midtread type. The quantizer input m can always be assumed to be a sample value of a zero-mean random variable M. (If the input has a nonzero mean, it can always be removed by subtracting the mean from the input and then adding it back With the input M having zero mean, and the quantizer after quantization.) assumed to be symmetric as in Figure 3.10, it follows that the quantizer output V and therefore the quantization error Q, will also have zero mean. Consider an input m of continuous amplitude in the range (-mmax, mmax). Assuming a uniform quantizer of the midrise type illustrated in Figure 3.10b, the step- size of the quantizer is given by & where L is the total number of representation levels and R denote the number of bits per sample used in the construction of the binary code. The probability density function of the quantization error Q is assumed to be uniform as follows: Pulse Code Modulation (PCM) In pulse-code modulation (PCM), a message signal is represented in discrete form in both time and amplitude. This form of signal representation permits the transmission of the message signal as a sequence of coded binary pulses. Given such a sequence, the effect of channel noise at the receiver output can be reduced to a negligible level simply by making the average power of the transmitted binary PCM wave large enough compared to the average power of the noise. Standard Telephone Speech Quantization The range of voltages covered by voice signals, from the peaks of loud talk to the weak passages of weak talk, is on the order of 1000 to 1. By using a nonunifom quantizer with the feature that the step-size increases as the separation from the origin of the input-output amplitude characteristic is increased, the large end steps of the quantizer can take care of possible departures of the voice signal into the large amplitude ranges that occur relatively infrequently. In other words, the weak passages, which need more protection, are favored at the expense of the loud passages. In this way, a nearly uniform percentage precision is achieved throughout the greater part of the amplitude range of the input signal, with the result that fewer steps are needed than would be the case if a uniform quantizer were used. The use of a nonuniform quantizer is equivalent to passing the baseband signal through a compressor and then applying the compressed signal to a uniform quantizer. There are tow particular forms of compression law that is used in practice are: µ law and A law which are defined respectively by To restore the signal samples to their correct relative level, a device in the receiver with a characteristic complementary to the compressor is used. Such a device is called an expander. The compression and expansion laws are exactly inverse so that, except for the effect of quantization, the expander output is equal to the compressor input. The combination of a compressor and an expander is called a compander. Where m and v are the normalized input and output voltages, µ and A are positive constants. The typical values used in practice are: µ = 255 and A = 87.6. It is also of interest to note that in actual PCM systems, the companding circuitry does not produce an exact replica of the nonlinear compression curves shown in Figure 3.14. Rather, it provides a piecewise linear approximation to the desired curve. By using a large enough number of linear segments, the approximation can approach the true compression curve very closely. Binary Encoding To exploit the advantages of sampling and quantizing for the purpose of making the transmitted signal more robust to noise, interference and other channel impairments, we require the use of an encoding process to translate the discrete set of sample values to a more appropriate form of signal. A particular arrangement of symbols used in a code to represent a single value of the discrete set is called a codeword or character. The two symbols of a binary code are customarily denoted as 0 and 1. in a binary code, each codeword consists of R bits. Thus R denotes the number of bits per sample. Then, using such a code, we may represent a total of 2R distinct samples. For example, a sample quantized into one of 256 levels may be represented by an 8-bit codeword. Line Coding (a) In unipolar NRZ signaling, symbol 1 is represented by transmitting a pulse of amplitude A for the duration of the symbol, and symbol 0 is represented by switching off the pulse (on-off signaling). Disadvantages of on-off signaling are the waste of power due to the transmitted DC level and the fact that the power spectrum of the transmitted signal does not approach zero at zero frequency. (b) in Polar NRZ signaling, symbols 1 and 0 are represented by transmitting pulses of amplitudes +A and -A, respectively. This line code is relatively easy to generate but its disadvantage is that the power spectrum of the signal is large near zero frequency. (c) in unipolar RZ signaling, symbol 1 is represented by a rectangular pulse of amplitude A and half-symbol width, and symbol 0 is represented by transmitting no pulse. An attractive feature of this line code is the presence of delta functions at f = 0, ±l/Tb in the power spectrum of the transmitted signal, which can be used for bit timing recovery at the receiver. However, its disadvantage is that it requires 3 dB more power than polar return-to-zero signaling for the same probability of symbol error (d) in bipolar RZ signaling, three amplitude levels are used. Specifically, positive and negative pulses of equal amplitude (i.e., +A and -A) are used alternately for symbol 1, with each pulse having a half-symbol width; no pulse is always used for symbol 0. A useful property of the BRZ signaling is that the power spectrum of the transmitted signal has no DC component and relatively insignificant low-frequency components for the case when symbols 1 and 0 occur with equal probability. (e) Split-phase (Manchester code) In this method of signaling, symbol 1 is represented by a positive pulse of amplitude A followed by a negative pulse of amplitude -A, with both pulses being half-symbol wide. For symbol 0, the polarities of these two pulses are reversed. The Manchester code suppresses the DC component and has relatively insignificant low-frequency components, regardless of the signal statistics. This property is essential in some applications. Regenerative Repeater The most important feature of PCM systems lies in the ability to control the effects of distortion and noise produced by transmitting a PCM signal through a channel. This capability is accomplished by reconstructing the PCM signal by means of a chain of regenerative repeaters located at sufficiently close spacing along the transmission route. The equalizer shapes the received pulses so as to compensate for the effects of amplitude and phase distortions produced by the no ideal channel. The timing circuitry provides a periodic pulse train, derived from the received pulses, for sampling the equalized pulses at the instants at time where the signal-to-noise ratio is a maximum. Each sample so extracted is compared to a predetermined threshold in the decision-making device. In each bit interval, a decision is then made whether the received symbol is a 1 or a 0 on the basis of whether the threshold is exceeded or not. If the threshold is exceeded, a clean new pulse representing symbol 1 is transmitted to the next repeater. Otherwise, another clean new pulse representing symbol 0 is transmitted. In practice, however, the regenerated signal departs from the original signal for two main reasons: 1. The unavoidable presence of channel noise and interference causes the repeater to make wrong decisions occasionally, thereby introducing bit errors into the regenerated signal. 2. If the spacing between received pulses deviates from its assigned value, a jitter is introduced into the regenerated pulse position, thereby causing distortion. PCM Receiver • Decoding: The first operation in the receiver is to regenerate (i.e., reshape and clean up) the received pulses one last time. These clean pulses are then regrouped into code words and decoded (i.e., mapped back) into a quantized PAM signal. • Filtering: The final operation in the receiver is to recover the message signal by passing the decoder output through a low-pass reconstruction filter whose cutoff frequency is equal to the message bandwidth B. Assuming that the transmission path is error free, the recovered signal includes no noise with the exception of the initial distortion introduced by the quantization process. Noise Considerations in PCM Systems The performance of a PCM system is influenced by two major sources of noise: 1. Channel noise, which is introduced anywhere between the transmitter output and the receiver input. Channel noise is always present, once the equipment is switched on. 2. Quantization noise, which is introduced in the transmitter. Unlike channel noise, quantization noise is signal dependent in the sense that it disappears when the message signal is switched off. Advantages of PCM In a generic sense, pulse-code modulation (PCM) has emerged as the most favored modulation scheme for the transmission of analog information-bearing signals such as voice and video signals. We may summarize the important advantages of PCM as follows: 1. Robustness to channel noise and interference. 2. Efficient regeneration of the coded signal along the transmission path. 3. Efficient exchange of increased channel bandwidth for improved signal-to- noise ratio, obeying an exponential law. 4. A uniform format for the transmission of different kinds of baseband signals, hence their integration with other forms of digital data in a common network. 5. Comparative ease with which message sources may be dropped or reinserted in a time-division multiplex system. 6. Secure communication through the use of special modulation schemes or encryption. These advantages, however, are attained at the cost of increased system complexity and increased channel bandwidth. T1 Carrier System The T1 system, which carries 24 voice channels over separate pairs of wires with regenerative repeaters spaced at approximately 2-km intervals. each of the 24 voice channels uses a binary code with an 8-bit word. The first bit indicates whether the input voice sample is positive (1) or negative (0). The next three bits of the code word identify a particular segment inside which the amplitude of the input voice sample lies, and the last four bits identify the actual representation level inside that segment. With a sampling rate of 8 kHz, each frame of the multiplexed signal occupies a period of 125 μsec. In particular, it consists of twenty-four 8- bit words, plus a single bit that is added at the end of the frame for the purpose of synchronization. Hence, each frame consists of a total of (24 x 8) + 1 = 193 bits. Correspondingly, the duration of each bit equals 0.647 μsec, and the resulting transmission rate is 1.544 megabits per second (Mb/s). Time Division Multiplexing (TDM) The T1 carrier (1.544 Mbps) TDM Hierarchy Multiplexing T1 streams into higher carriers T1 (DS1) consists of 24 Telephone calls T2 (DS2) consists of 24*4= 96 Telephone calls T3 (DS3) consists of 96*7=672 Telephone calls T4 (DS4) consists of 672*6= 4032 Telephone calls